Current terrestrial or satellite digital TV transmission channels are highly bandwidth constrained. This means that sophisticated modulation techniques must be employed to conserve bandwidth as much as possible. A common factor underlying the use of any of these sophisticated modulation techniques is the need to minimize noise and channel distortion in the TV receiver demodulation process. This is necessary in order to ensure accurate signal recovery. The need to minimize channel distortions in digital TV receivers often requires the use of equalization or deghosting networks. These networks usually employ digital filtering or other signal processing that involves numerous arithmetic multiplications. For example, coefficients of `m` bits in length are multiplied by data of `n` bits in length to produce data of `m+n` bits in length. It is often impractical and expensive to use a data bus width of `m+n` bits within the filter network. In practice, the data is usually truncated so that it is represented by fewer bits, and the least significant bits are discarded.
However, when data values are truncated, an average truncation error is introduced into the data. The average value of this error for a single truncation stage is equal to one half of the Least Significant Bit (LSB) of the truncated value. The truncation error appears as a DC bias in the resulting series of data values, and increases in proportion to the number of truncation stages that sequentially process the data. For instance, after "Y" truncation stages the resultant average DC offset component (hereafter termed the Offset Error) in the data is given by: EQU Offset Error=Y*LSB/2
where LSB is the Least Significant Bit of the truncated number.
This result assumes a constant scaling of data throughout the truncation stages. If truncations are performed at different scalings during processing, the Offset Error in the data is altered. Then the Offset Error equals the sum of the truncation errors at each stage. However, the truncation error at each stage equals the product of the LSB/2 truncation error multiplied by the appropriate scale factor at each stage.
The fact that the Offset Error is proportional to the number of truncation stages, assuming constant scaling, means that error accumulation occurs. Those systems performing a significant number of sequential truncations, such as TV receivers containing digital filters, are particularly susceptible to error accumulation. Error accumulation reduces the signal to noise ratio of the receiving system, which results in degraded receiver operation.